Visiting Fellow: Professor N. O. Santos

为了更深入地理解爱因斯坦的广义相对论，澄清某些精确解族的物理解释是很重要的，这些解族代表了圆柱对称或轴对称的时空。本文将研究三种情况：(1)具有微分旋转或微分平移的真空圆柱对称时空。(2)包含特定极限下史瓦西时空的奇异平稳轴对称时空族。(3)一种复合时空，其内部是哥德尔解所描述的旋转流体圆柱体，外部包含负的宇宙常数。在所有情况下，该项目的目的是研究这些解族的物理性质及其包含的参数的含义。

In seeking a deeper understanding of Einstein's theory of general relativity, it is important to clarify the physical interpretation of certain families of exact solutions which represent cylindrically or axially symmetric space-times. Three cases will be investigated: (1) A vacuum cylindrically symmetric space-time with differential rotation or translation. (2) A family of singular stationary axially symmetric space-times that includes the Schwarzschild space-time in a particular limit. (3) A compound space-time for which the interior is a cylinder of rotating fluid described by the Godel solution, and the exterior contains a negative cosmological constant. In all cases, the aim of the project is to investigate the physical properties of these families of solutions and the meaning of the parameters they contain.